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fubarobfusco comments on 0 And 1 Are Not Probabilities - Less Wrong

34 Post author: Eliezer_Yudkowsky 10 January 2008 06:58AM

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Comment author: fubarobfusco 29 July 2011 09:28:29AM -1 points [-]

Jaynes avoids P(A|B) for "probability of A given evidence B" and P(B) for "probability of B", preferring P(A|BX) and P(B|X) where X is one's background knowledge. This and the above leads naturally to the question of ~X: the situation in which one's "background knowledge" is false.

Assume that background knowledge X is the conjunction of a finite number of propositions. ~X is true if any of these propositions is false. If we can factor X into YZ where Y is the portion we suspect of being false — that is, if we can isolate for testing a portion of those beliefs we previously treated as "background knowledge" — then we can ask about P(A|BYZ) and P(A|B·~Y·Z).